Question

A race car moving along a circular track has a centripetal acceleration of 15.4^2. If the car has a tangential speed of 30 what is the distance between the car and the center of the track?

Answer 1

In uniform circular motion (circular motion at same speed), (tangential velocity)^2/radius = acceleration towards the center of the circle (centripetal acceleration) 
Also, radius is the distance to the center of the circle (track). 
So, in your case, 15.4m/s^2 = (30.0m/s)^2/(radius) 
radius = (900.m^2/s^2) / (15.4m/s^2) 
radius = 58.4m

Answer 2

Answer:

58.44m

Step-by-step explanation:

Centripetal acceleration in a circular path is defined as follows:

$a_{c}=\frac{v^2}{r}$

Where $a_{c}$ is the centripetal acceleration,  $v$ is the tangential speed, and  $r$ is the radius of the circle.

Since we need to know the distance between the car and the center of the track, we are looking for the radius of the circular track  $r$, so we clear for it in the last equation:

$r=\frac{v^2}{a_{c}}$

And since we have the following information:

centripetal acceleration: $a_{c}=15.4m/s^2$

tangential speed: $v=30m/s$

We substitute these values in the equation to find the radius:

$r=\frac{v^2}{a_{c}}=\frac{(30m/s)^2}{15.4m/s^2}=\frac{900m^2/s^2}{15.4m/s^2}=58.44m$

The distance between the car and the center of the track is 58.44m